[R] lme and aov

[Peter Dalgaard]

Gang Chen wrote:
> Thanks a lot for clarification! I just started to learn programming in 
> R for a week, and wanted to try a simple mixed design of balanced 
> ANOVA with a between-subject factor
> (Grp) and a within-subject factor (Rsp), but I'm not sure whether I'm 
> modeling the data correctly with either of the command lines.
>
> Here is the result. Any help would be highly appreciated.
>
> > fit.lme <- lme(Beta ~ Grp*Rsp, random = ~1|Subj, Model);
> > summary(fit.lme)
> Linear mixed-effects model fit by REML
> Data: Model
>       AIC      BIC    logLik
>   233.732 251.9454 -108.8660
>
> Random effects:
> Formula: ~1 | Subj
>         (Intercept)  Residual
> StdDev:    1.800246 0.3779612
>
> Fixed effects: Beta ~ Grp * Rsp
>                  Value Std.Error DF    t-value p-value
> (Intercept)  1.1551502 0.5101839 36  2.2641837  0.0297
> GrpB        -1.1561248 0.7215090 36 -1.6023706  0.1178
> GrpC        -1.2345321 0.7215090 36 -1.7110417  0.0957
> RspB        -0.0563077 0.1482486 36 -0.3798196  0.7063
> GrpB:RspB   -0.3739339 0.2096551 36 -1.7835665  0.0829
> GrpC:RspB    0.3452539 0.2096551 36  1.6467705  0.1083
> Correlation:
>           (Intr) GrpB   GrpC   RspB   GrB:RB
> GrpB      -0.707
> GrpC      -0.707  0.500
> RspB      -0.145  0.103  0.103
> GrpB:RspB  0.103 -0.145 -0.073 -0.707
> GrpC:RspB  0.103 -0.073 -0.145 -0.707  0.500
>
> Standardized Within-Group Residuals:
>         Min          Q1         Med          Q3         Max
> -1.72266114 -0.41242552  0.02994094  0.41348767  1.72323563
>
> Number of Observations: 78
> Number of Groups: 39
>
> > fit.aov <- aov(Beta ~ Rsp*Grp+Error(Subj/Rsp)+Grp, Model);
> > fit.aov
>
> Call:
> aov(formula = Beta ~ Rsp * Grp + Error(Subj/Rsp) + Grp, data = Model)
>
> Grand Mean: 0.3253307
>
> Stratum 1: Subj
>
> Terms:
>                      Grp
> Sum of Squares  5.191404
> Deg. of Freedom        1
>
> 1 out of 2 effects not estimable
> Estimated effects are balanced
>
> Stratum 2: Subj:Rsp
>
> Terms:
>                          Rsp
> Sum of Squares  7.060585e-05
> Deg. of Freedom            1
>
> 2 out of 3 effects not estimable
> Estimated effects are balanced
>
> Stratum 3: Within
>
> Terms:
>                       Rsp       Grp   Rsp:Grp Residuals
> Sum of Squares    0.33428  36.96518   1.50105 227.49594
> Deg. of Freedom         1         2         2        70
>
> Residual standard error: 1.802760
> Estimated effects may be unbalanced
>
This looks odd.  It is a standard split-plot layout, right? 3 groups of 
13 subjects, each measured with two kinds of Rsp = 3x13x2 = 78 
observations.

In that case you shouldn't see the same effect allocated to multiple 
error strata. I suspect you forgot to declare Subj as factor.

Also: summary(fit.aov) is nicer, and anova(fit.lme) should be informative.